Reconstruction and assessment of the least-squares and slope discrepancy components of the phase

The concept of slope discrepancy developed in the mid-1980's to assess meas urement noise in a wave-front sensor system is shown to have additional con tributions that are due to fitting error and branch points. This understand ing is facilitated by the development of a new formulation that employs Fou rier techniques to decompose the measured gradient field (i.e., wave-front sensor measurements) into two components, one that is expressed as the grad ient of a scalar potential and the other that is expressed as the curl of a vector potential. A key feature of the theory presented here is the fact t hat both components of the phase tone corresponding to each component of th e gradient field are easily reconstructable from the measured gradients. In addition, the scalar and vector potentials are both easily expressible in terms of the measured gradient field. The work concludes with a wave optics simulation example that illustrates the ease with which both components of the phase can be obtained. The results obtained illustrate that branch poi nt effects are not significant until the Rytov number is greater than 0.2. In addition, the branch point contribution to the phase not only is reconst ructed from the gradient data but is used to illustrate the significant per formance improvement that results when this contribution is included in the correction applied by an adaptive optics system. (C) 2000 Optical Society of America [S0740-3232(00)02210-9]. OCIS codes: 010.1080, 010.1300, 010.133 0, 010.7530.